Hybrid resampling method for fan beam spect

Abstract

A method of resampling of a sinogram from a fan beam SPECT includes the steps of angular resampling of the sinogram using frequency modulation, and thence transfers resampling of the sinogram using linear interpolation. This permits the use of parallel geometry algorithms in quantitative work without the expected degradation of resolution or the introduction of artifacts.

I claim: 
     
       1. A method of hybrid resampling of a sinogram from a fan beam SPECT, comprising the steps of: angular resampling of the sinogram using frequency modulation; and transverse resampling of the sinogram using linear interpolation.   
     
     
       2. The method of claim 1, wherein fan beam data is obtained from a symmetrical fan beam collimator in a circular orbit, wherein the data consists of a plurality of planar projections taken at M equiangular stops in 360°, wherein M is an integral power of 2, and wherein the step of angular resampling includes the steps of: A. taking the discrete fast fourier transform along columns of the sinogram with respect to the angular coordinate;   B. using frequency modulation based on the transform of step A to obtain a translation in sinogram space; and   C. inverse transforming the translation using the fast fourier transform.   
     
     
       3. The method of claim 1, wherein fan beam data is obtained from a symmetrical fan beam collimator in a circular orbit, wherein the data consists of a plurality of planar projections taken at M equiangular stops in 360°, wherein M is not an integral power of 2, and wherein the step of angular resampling includes the steps of: A. taking the discrete prime factor Z-transform based on the fast fourier transform along columns of the sinogram with respect to the angular coordinate;   B. using frequency modulation based on the transform of step A to obtain a translation in sinogram space; and   C. inverse transforming the translation using a prime factor fast fourier transform.   
     
     
       4. A method of reconstructing an object from sinograms from a fan beam SPECT, comprising the steps of: A. obtaining fan beam projection data from a symmetric fan beam collimator in a circular orbit;   B. resampling the fan beam projection data to parallel beam projection data, comprising the steps of: 1. angular resampling the sinogram using frequency modulation; and   2. transverse resampling the sinogram using linear interpolation;     C. correcting the parallel beam projection data for the transverse component of sensitivity;   D. generating contours based upon an algorithm that back projects edge information to form the contour of a convex body outline;   E. pre-multiplying, using an algorithm which accounts for the shadow of an off-center convex attenuating body;   F. taking the two-dimensional fourier transform of the sinogram;   G. removing the far field component of the sinogram; and   H. exponentially back projecting the projection data.